The present application generally relates to extremum seeking control strategies. The present application more particularly relates to regulating, via extremum seeking control, the amount of air that is flowing through a heating, ventilation and air conditioning (HVAC) system in order to reduce the amount of mechanical heating and cooling required within an air-handling unit (AHU).
Extremum seeking control (ESC) is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. It can be considered a dynamic realization of gradient searching through the use of dithering signals. The gradient of the system output with respect to the system input is typically obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using an integrator in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system.
Typical ESCs utilize a closed-loop configuration in which a gradient is calculated between the inputs to a plant and system performance. An integrator is then used in the closed-loop system to drive the gradient to zero. A detrimental phenomenon known as “integrator windup” may occur if the determined optimal reference point for the system is mathematically outside of the operating range for the actuator, causing the optimal settings for the actuator to correspond to an operating boundary. When the actuator cannot move to the optimal setting determined by the ESC loop, a condition known as actuator saturation is said to exist. For example, the optimal power consumption for an AHU utilizing an extremum seeking controller may correspond to a damper opening of less than 0%, a physical impossibility. When an actuator saturation condition exists, the integrator output will continue to grow until the sign of the input to the integrator changes.